My research interests primarily lie in mathematical finance, mean field theory, and the analysis of partial differential equations.
Specifically, I focus on portfolio selection in financial markets, mean field game/control problems and the mathematics of liquid crystals.
Publications/ Preprints:
(13). Consumption and investment in incomplete markets with Epstein-Zin preferences in infinite horizon
submitted, preprint available here (2026).
_________________________________________________________________________________________
(12). Local exact controllability of Landau-Lifshitz-Gilbert equation
with Chunxi Jiao,
submitted, preprint available here (2026).
_________________________________________________________________________________________
(11). Planar degenerate anchoring in Landau-de Gennes energy
with Yong Yu,
submitted, preprint available here (2026).
_________________________________________________________________________________________
(10). Optimal matching strategies in two-sided markets: A mean field approach
with Erhan Bayraktar, Dantong Chu and Bohan Li,
submitted, preprint available here (2025).
_________________________________________________________________________________________
(9). A variational approach to portfolio choice,
with Paolo Guasoni and Emmet Lawless,
submitted, preprint available here (2025).
_________________________________________________________________________________________
(8). Incentives of defined-contribution pension managers,
with Paolo Guasoni, Bohan Li, Tak Kwong Wong and Sheung Chi Phillip Yam,
submitted (2024).
_________________________________________________________________________________________
(7). Viscosity solutions of fully second-order HJB equations in the Wasserstein space, [Article]
with Erhan Bayraktar, Hang Cheung, Ibrahim Ekren, Jinniao Qiu and Xin Zhang,
SIAM Journal on Control and Optimization 64(4), 2250–2280 (2026).
_________________________________________________________________________________________
(6). A control theoretical approach to mean field games. Part II: global well-posedness of master equations, [Article]
with Alain Bensoussan, Tak Kwong Wong and Sheung Chi Phillip Yam,
Applied Mathematics and Optimization 93(45) (2026).
_________________________________________________________________________________________
(5). A control theoretical approach to mean field games. Part I: global equilibrium solution, [Article]
with Alain Bensoussan, Tak Kwong Wong and Sheung Chi Phillip Yam,
Applied Mathematics and Optimization 92(44) (2025).
_________________________________________________________________________________________
(4). Mean field type control problems, some Hilbert-space-valued FBSDEs, and related equations, [Article]
with Alain Bensoussan and Sheung Chi Phillip Yam,
ESAIM: Control, Optimisation and Calculus of Variations 31:33 (2025).
_________________________________________________________________________________________
(3). Viscosity solutions of a class of second order Hamilton-Jacobi-Bellman equations in the Wasserstein space, [Article]
with Hang Cheung and Jinniao Qiu,
Applied Mathematics and Optimization 91(23) (2025).
_________________________________________________________________________________________
(2). Pattern formation in Landau-de Gennes theory, [Article]
with Yong Yu,
Journal of Functional Analysis 285(1), 109923 (2023).
_________________________________________________________________________________________
(1). Singular solutions to some semilinear elliptic equations: an approach of Born-Infeld approximation, [Article]
with Chia-Yu Hsieh and Yong Yu,
Communications in Mathematical Sciences 19(2), 557–584 (2021).